Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!ncsu!uvacs!gmf
From: gmf@uvacs.UUCP
Newsgroups: net.math
Subject: Interesting Numbers
Message-ID: <1292@uvacs.UUCP>
Date: Thu, 10-May-84 09:34:10 EDT
Article-I.D.: uvacs.1292
Posted: Thu May 10 09:34:10 1984
Date-Received: Sat, 12-May-84 12:54:43 EDT
Lines: 20


>>  Any number n is interesting because it is the least positive integer
>>  with the property of being greater than n-1.  This is absurd.  Not
>>  all properties are interesting.

But are all *numbers* interesting?  Is it true that for any number n,
there is a property P such that P(n) and P(n) implies n is interesting?

Every number n has the property that it is an element of a set of which
it is the least member, namely singleton n.  I say this is interesting
(although only mildly).  Thus all numbers are interesting.  Admittedly,
induction is de trop, not to say downright de ceptive.

If it is not true that for any number n, there is a property P such that
P(n) and P(n) implies n, then there is a number n such that for every
property P , if P(n) then P(n) does not imply n is interesting.  In
short, there is a number which does not have a property which makes
it interesting.  That would be a very interesting number.

     Gordon Fisher